Lie groups of measurable mappings

We describe new construction principles for infinite-dimensional Lie groups. In particular, given any measure space (X, Sigma, mu) and (possibly infinite-dimensional) Lie group G, we construct a Lie group L-infinity (X, G), which is a Frechet-Lie group if G is so. We also show that the weak direct product Pi(iis an element ofI)* G(i) of an arbitrary family (G(i))(iis an element ofI) of Lie groups can be made a Lie group, modelled on the locally convex direct sum circle plus(iis an element ofI) L(G(i)).